1. Field of the Invention
The present invention relates to an estimating method for a road friction coefficient μ, and more particularly to an estimating method for a road friction coefficient μ in which the road friction coefficient μ can be easily computed and a practical accuracy of estimation can be ensured. Further, the present invention relates to a vehicle slip angle estimating method, and more particularly to a vehicle slip angle estimating method for estimating a vehicle slip angle by regressively using a previous estimated value of the vehicle slip angle in calculating a present estimated value of the vehicle slip angle on the basis of a vehicle dynamic model calculated by the road friction coefficient μ.
2. Description of the Related Art
In controlling a motional condition of a vehicle, such as a turning motion, it is known to improve the vehicle dynamics by using an angle (slip angle β) formed between a running direction of the vehicle and a longitudinally extending center line of the vehicle to perform optimum torque distribution control or the like.
As a method of estimating a slip angle β, Patent Document of Japanese Patent Publication No. 2003-306092 discloses a slip angle estimating method using a lateral force acting on a rear wheel in a lateral direction of a vehicle on the basis of a tire dynamic model.
According to the method disclosed in Japanese Patent Publication No. 2003-306092, a road friction coefficient μ is first estimated by performing proportional-integral-derivative (PID) action to calculate an adjusting value for adjusting an initial value of the road friction coefficient μ so that the difference between a lateral acceleration detected by a lateral acceleration sensor and a lateral acceleration estimated according to a previous estimated value of a slip angle derivative β′, a detected vehicle speed V, and a detected yaw rate r becomes zero, and then adding the adjusting value calculated above to the initial value near 1.
A lateral force (tire lateral force Yr) acting on a rear wheel is calculated by using an estimated value of the road friction coefficient μ and a previous estimated value of the slip angle β on the basis of a tire dynamic model. Then, the tire lateral force Yr calculated above, an angular velocity (yaw rate r) about a vertical axis passing through the center of gravity of the vehicle as detected by a yaw rate sensor, a derivative r′ of the yaw rate r, and a vehicle speed V detected by a vehicle speed sensor are inserted into Eq. (1) shown below to estimate a derivative (slip angle derivative β′) of the slip angle β with respect to time.β′=−2(Lf+Lr)Yr/mVLf+Ir′/mVLf−r−M/mVLf   (1)where Lf is the distance from the center of gravity of the vehicle to the front axle, Lr is the distance from the center of gravity of the vehicle to the rear axle, Yr is the tire lateral force, r′ is the yaw rate derivative, m is the total mass of the vehicle, I is the yawing moment of inertia, and M is the yawing moment.
An estimated value of the slip angle derivative β′ is integrated with respect to time to estimate a present value of the slip angle β. By using the present estimated value of the slip angle derivative β′, a lateral acceleration is estimated. Further, by regressively using the present estimated value of the slip angle β, a next value of the tire lateral force Yr is calculated, and by using this next value of the tire lateral force Yr, next values of the slip angle derivative β′ and the slip angle β are estimated.
As mentioned above, integration is performed by an integrator provided in a PID controller in estimating the road friction coefficient μ, and the slip angle derivative β′ is integrated by another integrator in estimating the slip angle β. Thus, the two integrators are used for the estimation of the road friction coefficient μ and the slip angle.
A signal to be integrated includes a sensor signal from a vehicle, so that the result of integration includes noise and error, which are accumulated by the integration. Accordingly, the accuracy of estimation may be greatly reduced. In particular, the two integrators are used for the estimation of the road friction coefficient μ and the slip angle as mentioned above, and the result of integration obtained in estimating one of the road friction coefficient μ and the slip angle is utilized for the estimation of the other. As a result, it is considered that neither the slip angle β nor the road friction coefficient μ may mathematically converge to true values.
If the slip angle β cannot be accurately estimated, the motional condition of a vehicle to be controlled by using the slip angle cannot be accurately controlled. Accordingly, it is desirable that an estimated value of the slip angle is not to be used for the estimation of the road friction coefficient μ or that the influence of the estimated value of the slip angle is to be suppressed in the case of using the estimated value.
In the conventional vehicle slip angle estimating method mentioned above, the slip angle derivative β′ and the slip angle β are calculated regardless of values of the vehicle speed V. As shown in Eq. (1), however, the vehicle speed V is included in the denominators of the first, second, and fourth terms, so that when the vehicle speed V is decreased, the denominators of the first, second, and fourth terms are decreased and the reciprocal of the vehicle speed V is therefore increased. Further, the increased reciprocal of the vehicle speed V is multiplied by sensor noise or the like to cause a remarkable influence of such sensor noise or the like. Thus, when the vehicle speed V is qualitatively low, the slip angle derivative β′ becomes large in error. Accordingly, the slip angle β as an integral of the slip angle derivative β′ includes a large error.
Further, the present estimated value of the slip angle β is calculated by regressively using the previous estimated value of the slip angle β including a large error, and a lateral acceleration is estimated by regressively using the previous estimated value of the slip angle derivative β′. Accordingly, the errors included in the present estimated values of the slip angle derivative β′ and the slip angle β are superimposed to become larger. As a result, the estimated values of the slip angle derivative β′ and the slip angle β are changed in sign at a frequency of 3 Hz or higher which is inconceivable in a usual vehicle motion, so that the estimated values of the slip angle derivative β′ and the slip angle β are diverged.
FIGS. 20A, 20B, and 20C are graphs showing the divergence of the slip angle β. In FIG. 20A, the vertical axis represents vehicle speed V, and the horizontal axis represents time t. In FIG. 20B, the vertical axis represents slip angle β, and the horizontal axis represents time t. In FIG. 20C, the vertical axis represents estimated lateral acceleration Gye, and the horizontal axis represents time t. As shown in FIG. 20A, the vehicle speed is increased from zero at the time t0 and thereafter decreased to zero at the time t3.
As shown in FIGS. 20A and 20B, there is a problem such that the estimated value of the slip angle β is changed in sign at a frequency of 3 Hz or higher to cause divergence during a period from the time t0 to the time t1 at which the vehicle speed V reaches a certain speed in increasing the vehicle speed V and during a period from the time t2 at which the vehicle speed V reaches a certain speed in decreasing the vehicle speed V to the time t3. Further, as shown in FIG. 20C, the estimated lateral acceleration Gye calculated by using the slip angle derivative β′ is also diverged.
Such divergence occurs not only in the vehicle slip angle estimating method using Eq. (1), but also in any other methods of estimating the vehicle slip angle by regressively using the previous estimated value of the vehicle slip angle in calculating the present estimated value of the vehicle slip angle on the basis of a vehicle dynamic model.
The motional condition of the vehicle is controlled by torque control with electromagnetic actuators for the front and rear wheels by using the slip angle β. Accordingly, the divergence of the slip angle β causes large variations in control command, resulting in an increase in frequency of operation of the electromagnetic actuators and the instability of the vehicle behavior. Therefore, the motional condition of the vehicle cannot be well controlled.